Department of Homeland Security officials tell NBC News that around 300 children have been moved from the Border Patrol facility in Clint, some of them to a tent detention camp under Border Patrol control where they will be held until they can be placed with the Department of Health and Human Services.

Others have been sent to a shelter system run by the DHHS's Office of Refugee Resettlement, department spokeswoman Elizabeth Stauffer tells the New York Times.

Rep. Veronica Escobar said Monday that around 30 children are still in the Clint facility, which had been severely overcrowded, the AP reports.

Lawyer Elora Mukherjee says that when she visited the Clint facility, she discovered unaccompanied children as young as seven or eight looking after toddlers.

"I have never seen conditions as appalling as what we witnessed last week," she said. "The children are hungry, dirty, and sick and being detained for very long periods of time." Mukherjee says none of the children had access to soap or toothpaste.

Some children had been there for close to a month, though government rules state that children should only be held in Border Patrol facilities for up to 72 hours.

The Times reports that strain on the DHHS system began to ease last week after Mexico took stronger measures to prevent border crossings—and the department relaxed a policy that required family members seeking to sponsor the children to provide fingerprints.